Solve 36^3*15^2/18^4*10^3*O

$$\frac { 36 ^ { 3 } \cdot 15 ^ { 2 } } { 18 ^ { 4 } \cdot 10 ^ { 3 } } \cdot O$$

Evaluate

$$\frac{O}{10}$$

Solution Steps

Calculate 36 to the power of 3 and get 46656.

$$\frac{46656\times 15^{2}}{18^{4}\times 10^{3}}O$$

Calculate 15 to the power of 2 and get 225.

$$\frac{46656\times 225}{18^{4}\times 10^{3}}O$$

Multiply 46656 and 225 to get 10497600.

$$\frac{10497600}{18^{4}\times 10^{3}}O$$

Calculate 18 to the power of 4 and get 104976.

$$\frac{10497600}{104976\times 10^{3}}O$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{10497600}{104976\times 1000}O$$

Multiply 104976 and 1000 to get 104976000.

$$\frac{10497600}{104976000}O$$

Reduce the fraction \frac{10497600}{104976000} to lowest terms by extracting and canceling out 10497600.

$$\frac{1}{10}O$$

Differentiate w.r.t. O

$$\frac{1}{10} = 0.1$$

Steps Using Definition of a Derivative

Calculate 36 to the power of 3 and get 46656.

$$\frac{\mathrm{d}}{\mathrm{d}O}(\frac{46656\times 15^{2}}{18^{4}\times 10^{3}}O)$$

Calculate 15 to the power of 2 and get 225.

$$\frac{\mathrm{d}}{\mathrm{d}O}(\frac{46656\times 225}{18^{4}\times 10^{3}}O)$$

Multiply 46656 and 225 to get 10497600.

$$\frac{\mathrm{d}}{\mathrm{d}O}(\frac{10497600}{18^{4}\times 10^{3}}O)$$

Calculate 18 to the power of 4 and get 104976.

$$\frac{\mathrm{d}}{\mathrm{d}O}(\frac{10497600}{104976\times 10^{3}}O)$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{\mathrm{d}}{\mathrm{d}O}(\frac{10497600}{104976\times 1000}O)$$

Multiply 104976 and 1000 to get 104976000.

$$\frac{\mathrm{d}}{\mathrm{d}O}(\frac{10497600}{104976000}O)$$

Reduce the fraction \frac{10497600}{104976000} to lowest terms by extracting and canceling out 10497600.

$$\frac{\mathrm{d}}{\mathrm{d}O}(\frac{1}{10}O)$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{1}{10}O^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{10}O^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{1}{10}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{10}$$